SEOUL—North Korea’s latest tirade, threatening to shelve inter-Korean talks unless Seoul ends U.S. military exercises and muzzles public criticism of the North, heralds a shift toward a more strident tone from Pyongyang that will test Washington and Seoul’s willingness to engage with the North.

Pyongyang’s latest statement, which slammed South Korea’s liberal government as “an ignorant and incompetent group devoid of the elementary sense of the present situation,” adds more uncertainty to a thaw in relations with the U.S....